Group #26118886 — subgroups

Subgroups — #26118886

Order 12032.

574 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689503	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689408	C₂	1	2	yes	maximal
3	C₂×#15688870	C₂	1	2	yes	maximal
4	#20241223	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1984	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₈₈	—	2	2	no	—
7	C₂×#13094024	C₂²	1	2	yes	—
8	#15689503	—	2	4	no	—
9	#15689408	—	2	4	no	—
10	#15689408	—	2	4	no	—
11	C₂×#13093955	—	2	2	no	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×#13093948	—	2	2	no	—
14	#15688870	—	2	4	no	—
15	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#336	—	2	2	no	—
19	C₂²×Dic₉₄	—	2	2	no	—
20	C₂×Dic₁₈₈	—	2	8	no	—
21	C₂×Dic₁₈₈	—	4	4	no	—
22	C₂×Dic₁₈₈	—	4	4	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	#13094024	—	2	2	no	—
25	#13094024	—	2	2	no	—
26	#13094024	—	2	2	no	—
27	#13094024	D₄	1	4	yes	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	#13093955	—	2	8	no	—
31	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
32	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
33	#13093948	—	2	8	no	—
34	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₄₇	—	2	1	no	—
36	C₂²×C₈×C₄₇	D₄	1	2	yes	—
37	C₄×Q₈×C₄₇	—	2	2	no	—
38	C₄×Q₈×C₄₇	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
40	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₄₇	—	2	1	no	—
42	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₄₇	—	2	2	no	—
44	C₄×C₈×C₄₇	—	2	2	no	—
45	C₂×Q₈×C₄₇	—	2	1	no	—
46	C₂×Q₈×C₄₇	—	2	2	no	—
47	C₂×Q₈×C₄₇	—	2	2	no	—
48	C₂×Q₈×C₄₇	Q₁₆	1	2	yes	complemented
49	C₂²×C₄×C₄₇	—	2	1	no	—
50	C₂²×C₄×C₄₇	—	2	1	no	—
51	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
54	C₂²×Dic₄₇	—	4	2	no	—
55	C₂×Dic₉₄	—	2	4	no	—
56	C₂×Dic₉₄	—	4	4	no	—
57	C₂×Dic₉₄	—	4	4	no	—
58	C₂×Dic₉₄	—	4	2	no	—
59	C₂×C₈×C₄₇	—	2	2	no	—
60	C₂×C₈×C₄₇	—	2	2	no	—
61	C₂×C₈×C₄₇	—	4	1	no	—
62	C₂×C₈×C₄₇	—	4	2	no	—
63	C₂×C₈×C₄₇	SD₁₆	1	4	yes	—
64	C₄⋊C₄×C₄₇	—	2	2	no	—
65	C₄⋊C₄×C₄₇	—	4	2	no	—
66	C₄²×C₄₇	—	4	1	no	—
67	C₄²×C₄₇	—	4	1	no	—
68	C₄²×C₄₇	C₂×D₄	1	2	yes	—
69	C₄²×C₄₇	C₂×D₄	1	2	yes	—
70	C₄⋊Dic₄₇	—	2	4	no	—
71	C₄⋊Dic₄₇	—	2	4	no	—
72	C₄⋊Dic₄₇	—	4	2	no	—
73	C₄⋊Dic₄₇	—	4	2	no	—
74	C₂×C₄₇⋊C₈	—	2	4	no	—
75	C₂×C₄₇⋊C₈	—	4	2	no	—
76	C₂×C₄₇⋊C₈	—	4	2	no	—
77	Dic₁₈₈	—	4	16	no	—
78	C₂³×C₄₇	#121	1	1	yes	characteristic
79	Q₈×C₄₇	—	2	4	no	—
80	Q₈×C₄₇	—	4	2	no	—
81	C₂×C₄×C₄₇	—	2	2	no	—
82	C₂×C₄×C₄₇	—	2	2	no	—
83	C₂×C₄×C₄₇	—	4	1	no	—
84	C₂×C₄×C₄₇	—	4	1	no	—
85	C₂×C₄×C₄₇	—	4	1	no	—
86	C₂×C₄×C₄₇	—	4	2	no	—
87	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
88	C₂×C₄×C₄₇	#120	1	2	yes	—
89	C₂×C₄×C₄₇	#121	1	2	yes	—
90	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
91	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
92	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
93	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
94	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
95	C₂×C₄×C₄₇	#137	1	2	yes	—
96	C₂×Dic₄₇	—	4	4	no	—
97	C₂×Dic₄₇	—	8	4	no	—
98	Dic₉₄	—	4	8	no	—
99	Dic₉₄	—	8	2	no	—
100	Dic₉₄	—	8	2	no	—
101	C₈×C₄₇	—	2	4	no	—
102	C₈×C₄₇	—	8	1	no	—
103	C₄₇⋊C₈	—	4	4	no	—
104	#10276	—	47	1	no	maximal, Sylow
105	C₂²×C₄₇	#392	1	1	yes	characteristic
106	C₂²×C₄₇	#460	1	2	yes	—
107	C₂²×C₄₇	#467	1	1	yes	characteristic
108	C₂²×C₄₇	#470	1	1	yes	characteristic
109	C₂²×C₄₇	#473	1	2	yes	—
110	C₄×C₄₇	—	2	2	no	—
111	C₄×C₄₇	—	4	2	no	—
112	C₄×C₄₇	—	8	1	no	—
113	C₄×C₄₇	#450	1	2	yes	—
114	C₄×C₄₇	#451	1	2	yes	—
115	C₄×C₄₇	#452	1	2	yes	—
116	C₄×C₄₇	#492	1	1	yes	characteristic
117	C₄×C₄₇	#496	1	1	yes	characteristic
118	Dic₄₇	—	8	4	no	—
119	C₂×#494	—	47	1	no	—
120	C₂×#475	—	47	2	no	—
121	#1984	D₄₇	1	1	yes	characteristic
122	C₂×#332	—	47	2	no	—
123	#1277	—	47	1	no	—
124	C₂×C₄₇	#1670	1	2	yes	—
125	C₂×C₄₇	#1690	1	2	yes	—
126	C₂×C₄₇	#2001	1	1	yes	characteristic
127	C₂×C₄₇	#2014	1	1	yes	characteristic
128	C₂×C₄₇	#2020	1	1	yes	characteristic
129	C₂²×Q₁₆	—	94	2	no	—
130	C₂×C₄⋊Q₈	—	47	2	no	—
131	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
132	#494	—	94	4	no	—
133	#475	—	94	4	no	—
134	#475	—	94	4	no	—
135	C₂×#106	—	94	2	no	—
136	C₂×C₄⋊C₈	—	47	2	no	—
137	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
138	C₂×#103	—	94	2	no	—
139	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
140	#336	—	2	2	no	—
141	#332	—	94	4	no	—
142	C₄₇	#10276	1	1	yes	characteristic, complemented, Sylow
143	C₂²×Q₈	—	94	2	no	—
144	C₂²×Q₈	D₁₈₈	1	1	yes	characteristic
145	C₂×Q₁₆	—	94	8	no	—
146	C₂×Q₁₆	—	188	4	no	—
147	C₂×Q₁₆	—	188	4	no	—
148	C₂²×C₈	—	2	1	no	—
149	C₂²×C₈	—	94	2	no	—
150	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
151	C₄⋊Q₈	—	47	4	no	—
152	C₄⋊Q₈	—	94	2	no	—
153	C₄⋊Q₈	—	94	2	no	—
154	C₄⋊Q₈	—	94	2	no	—
155	C₄×Q₈	—	2	2	no	—
156	C₄×Q₈	—	2	2	no	—
157	C₂×C₄⋊C₄	—	2	1	no	—
158	C₂×C₄⋊C₄	—	94	2	no	—
159	C₂×C₄⋊C₄	—	94	2	no	—
160	C₂×C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
161	C₂×C₄²	—	2	1	no	—
162	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
163	#106	—	94	8	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	47	4	no	—
166	C₄⋊C₈	—	94	2	no	—
167	#103	—	94	8	no	—
168	C₄×C₈	—	2	2	no	—
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	2	2	no	—
172	C₂×Q₈	—	94	4	no	—
173	C₂×Q₈	—	188	4	no	—
174	C₂×Q₈	—	188	4	no	—
175	C₂×Q₈	—	188	2	no	—
176	C₂×Q₈	Dic₁₈₈	1	2	yes	complemented
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	—	188	2	no	—
180	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
181	C₂²×C₄	#10625350	1	1	yes	characteristic
182	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
183	Q₁₆	—	188	16	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	—	4	1	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	94	4	no	—
189	C₂×C₈	—	188	2	no	—
190	C₂×C₈	—	188	2	no	—
191	C₂×C₈	#10625336	1	4	yes	—
192	C₄⋊C₄	—	2	2	no	—
193	C₄⋊C₄	—	4	2	no	—
194	C₄⋊C₄	—	94	4	no	—
195	C₄⋊C₄	—	94	4	no	—
196	C₄⋊C₄	—	188	2	no	—
197	C₄⋊C₄	—	188	2	no	—
198	C₄²	—	4	1	no	—
199	C₄²	—	4	1	no	—
200	C₄²	D₄×D₄₇	1	2	yes	—
201	C₄²	D₄×D₄₇	1	2	yes	—
202	C₂³	#13093998	1	1	yes	characteristic
203	Q₈	—	2	4	no	—
204	Q₈	—	4	2	no	—
205	Q₈	—	376	2	no	—
206	Q₈	—	376	2	no	—
207	Q₈	—	188	8	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	376	4	no	—
215	C₂×C₄	—	188	4	no	—
216	C₂×C₄	#13093992	1	1	yes	characteristic
217	C₂×C₄	#13093994	1	2	yes	—
218	C₂×C₄	#13093997	1	2	yes	—
219	C₂×C₄	#13094020	1	1	yes	characteristic
220	C₂×C₄	C₂×#10625336	1	2	yes	—
221	C₂×C₄	C₂×Dic₁₈₈	1	1	yes	characteristic
222	C₂×C₄	#13094046	1	1	yes	characteristic
223	C₂×C₄	#13094049	1	2	yes	—
224	C₂×C₄	#13094057	1	2	yes	—
225	C₈	—	2	4	no	—
226	C₈	—	8	1	no	—
227	C₈	—	188	4	no	—
228	C₂²	#15689032	1	1	yes	characteristic
229	C₂²	#15689323	1	2	yes	—
230	C₂²	#15689364	1	1	yes	characteristic
231	C₂²	#15689381	1	1	yes	characteristic
232	C₂²	#15689398	1	2	yes	—
233	C₄	—	2	2	no	—
234	C₄	—	4	2	no	—
235	C₄	—	8	1	no	—
236	C₄	—	376	4	no	—
237	C₄	#15689273	1	2	yes	—
238	C₄	#15689281	1	2	yes	—
239	C₄	#15689287	1	2	yes	—
240	C₄	#15689497	1	1	yes	characteristic
241	C₄	#15689513	1	1	yes	characteristic
242	C₂	#20242758	1	2	yes	—
243	C₂	#20242882	1	2	yes	—
244	C₂	#20244398	1	1	yes	characteristic
245	C₂	#20244475	1	1	yes	characteristic
246	C₂	#20244509	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689503

C₂

yes

maximal, characteristic

C₂×#15689408

C₂

yes

maximal

C₂×#15688870

C₂

yes

maximal

#20241223

C₂

yes

maximal, characteristic

C₄₇×#1984

C₂

yes

maximal, characteristic

C₂²×Dic₁₈₈

—

C₂×#13094024

C₂²

yes

—

—

—

—

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂×#13093948

—

#15688870

—

C₂×C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#336

—

C₂²×Dic₉₄

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂²×C₄₇⋊C₈

—

—

—

—

D₄

yes

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

#13093955

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

#13093948

—

C₂²×Q₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

D₄

yes

—

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄×C₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

Q₁₆

yes

complemented

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

characteristic

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

SD₁₆

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

—

C₂³×C₄₇

#121

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

#120

yes

—

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

#127

yes

characteristic

C₂×C₄×C₄₇

C₂×SD₁₆

yes

—

C₂×C₄×C₄₇

C₂×Q₁₆

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

100

Dic₉₄

—

101

C₈×C₄₇

—

102

C₈×C₄₇

—

103

C₄₇⋊C₈

—

104

#10276

—

maximal, Sylow

105

C₂²×C₄₇

#392

yes

characteristic

106

C₂²×C₄₇

#460

yes

—

107

C₂²×C₄₇

#467

yes

characteristic

108

C₂²×C₄₇

#470

yes

characteristic

109

C₂²×C₄₇

#473

yes

—

110

C₄×C₄₇

—

111

C₄×C₄₇

—

112

C₄×C₄₇

—

113

C₄×C₄₇

#450

yes

—

114

C₄×C₄₇

#451

yes

—

115

C₄×C₄₇

#452

yes

—

116

C₄×C₄₇

#492

yes

characteristic

117

C₄×C₄₇

#496

yes

characteristic

118

Dic₄₇

—

119

C₂×#494

—

120

C₂×#475

—

121

#1984

D₄₇

yes

characteristic

122

C₂×#332

—

123

#1277

—

124

C₂×C₄₇

#1670

yes

—

125

C₂×C₄₇

#1690

yes

—

126

C₂×C₄₇

#2001

yes

characteristic

127

C₂×C₄₇

#2014

yes

characteristic

128

C₂×C₄₇

#2020

yes

characteristic

129

C₂²×Q₁₆

—

130

C₂×C₄⋊Q₈

—

131

C₂×C₄×Q₈

C₂×D₄₇

yes

characteristic

132

#494

—

133

#475

—

134

#475

—

135

C₂×#106

—

136

C₂×C₄⋊C₈

—

137

C₂×C₄⋊C₈

C₂×D₄₇

yes

characteristic

138

C₂×#103

—

139

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

140

#336

—

141

#332

—

142

C₄₇

#10276

yes

characteristic, complemented, Sylow

143

C₂²×Q₈

—

144

C₂²×Q₈

D₁₈₈

yes

characteristic

145

C₂×Q₁₆

—

146

C₂×Q₁₆

—

188

—

147

C₂×Q₁₆

—

188

—

148

C₂²×C₈

—

149

C₂²×C₈

—

150

C₂²×C₈

C₂²⋊D₄₇

yes

—

151

C₄⋊Q₈

—

152

C₄⋊Q₈

—

153

C₄⋊Q₈

—

154

C₄⋊Q₈

—

155

C₄×Q₈

—

156

C₄×Q₈

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

D₁₈₈

yes

characteristic

161

C₂×C₄²

—

162

C₂×C₄²

C₂²×D₄₇

yes

characteristic

163

#106

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

#103

—

168

C₄×C₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

188

—

174

C₂×Q₈

—

188

—

175

C₂×Q₈

—

188

—

176

C₂×Q₈

Dic₁₈₈

yes

complemented

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

188

—

180

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

181

C₂²×C₄

#10625350

yes

characteristic

182

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

183

Q₁₆

—

188

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

188

—

190

C₂×C₈

—

188

—

191

C₂×C₈

#10625336

yes

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

188

—

197

C₄⋊C₄

—

188

—

198

C₄²

—

199

C₄²

—

200

C₄²

D₄×D₄₇

yes

—

201

C₄²

D₄×D₄₇

yes

—

202

C₂³

#13093998

yes

characteristic

203

Q₈

—

204

Q₈

—

205

Q₈

—

376

—

206

Q₈

—

376

—

207

Q₈

—

188

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

376

—

215

C₂×C₄

—

188

—

216

C₂×C₄

#13093992

yes

characteristic

217

C₂×C₄

#13093994

yes

—

218

C₂×C₄

#13093997

yes

—

219

C₂×C₄

#13094020

yes

characteristic

220

C₂×C₄

C₂×#10625336

yes

—

221

C₂×C₄

C₂×Dic₁₈₈

yes

characteristic

222

C₂×C₄

#13094046

yes

characteristic

223

C₂×C₄

#13094049

yes

—

224

C₂×C₄

#13094057

yes

—

225

C₈

—

226

C₈

—

227

C₈

—

188

—

228

C₂²

#15689032

yes

characteristic

229

C₂²

#15689323

yes

—

230

C₂²

#15689364

yes

characteristic

231

C₂²

#15689381

yes

characteristic

232

C₂²

#15689398

yes

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

376

—

237

C₄

#15689273

yes

—

238

C₄

#15689281

yes

—

239

C₄

#15689287

yes

—

240

C₄

#15689497

yes

characteristic

241

C₄

#15689513

yes

characteristic

242

C₂

#20242758

yes

—

243

C₂

#20242882

yes

—

244

C₂

#20244398

yes

characteristic

245

C₂

#20244475

yes

characteristic

246

C₂

#20244509

yes

characteristic

	subgroup	G/H
center	C₂³	#13093998
commutator, cosocle	C₂×C₄²×C₄₇	C₂³
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1984	C₂
socle, prime radical	C₂³×C₄₇	#121
hypercenter	#1984	D₄₇
hypocenter	C₄₇	#10276
LCS	G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

subgroup

G/H

center

C₂³

#13093998

commutator, cosocle

C₂×C₄²×C₄₇

C₂³

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1984

C₂

C₂³×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

N	H ≅ G/N	type
48. C₂×Q₈×C₄₇	Q₁₆	semidirect
142. C₄₇	#10276	semidirect
176. C₂×Q₈	Dic₁₈₈	semidirect

H ≅ G/N

type

48. C₂×Q₈×C₄₇

Q₁₆

semidirect

142. C₄₇

#10276

semidirect

176. C₂×Q₈

Dic₁₈₈

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#15689503	2
C₂×#15689408	2
C₂×#15688870	2
#20241223	2
C₄₇×#1984	2
#10276	47

subgroup

index

C₄₇×#1984

Subgroups — #26118886

Conjugacy classes of subgroups

Complements

Maximal subgroups